1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
daser333 [38]
2 years ago
6

Evelyn can run 3 miles in 40 minutes

Mathematics
1 answer:
hram777 [196]2 years ago
5 0

Answer:

m= 4.5 miles

Step-by-step explanation:

Let the number of miles Evelyn can run be m and can be modeled by the equation below

m= kx

Where x Is the Minutes

When m= 3

x= 40

3= k40

k= 3/40

If x= 60

m=3/40(60)

m = (60*3)/40

m= 180/40

m= 4.5 miles

You might be interested in
It is desired to pile some logs in layers so that the top layer contains one log, the next layer contains two logs, the next lay
Hitman42 [59]

Answer:

Yes all of the logs can be used in such a grouping.

We'll have <u>19 logs</u> in the bottom row (and have 19 rows)

========================================================

Explanation:

Let n be the number of layers. Let T(n) represent how many logs there are total.

  • If you have 1 layer, then you have 1 log. So we can say that T(1) = 1.
  • If there are n = 2 layers, then we have 1 log on top of two other logs, which leads to 1+2 = 3 logs total. This shows that T(2) = 3.
  • If there are n = 3 layers, then we have 1 log on top of 2 which are on top of 3 at the very bottom. We have 1+2+3 = 6 logs total. So T(3) = 6.
  • Having n = 4 layers gives 1+2+3+4 = 10 logs. So T(4) = 10
  • Having n = 5 layers gives 1+2+3+4+5 = 15 logs. So T(5) = 15

This process continues for however long you like. The sequence 1,3,6,10,15 is the set of triangular numbers, since the logs form a triangular or pyramid shape when stacked this way. To get the nth value in the triangular number sequence, use this formula

T(n) = 0.5*n*(n+1)

---------------

For example, let's say we wanted to find how many logs there were in the fifth layer

T(n) = 0.5*n*(n+1)

T(5) = 0.5*5*(5+1)

T(5) = 15

This matches from earlier.

The purpose of bringing in a formula is to see if we can get T(n) = 190 for some integer n.

-------------------

T(n) = 0.5*n*(n+1)

190 = 0.5*n*(n+1)

190*2 = n(n+1)

380 = n^2+n

0 = n^2+n-380

n^2+n-180 = 0

Applying the quadratic formula will lead to the two solutions: n = -20 and n = 19. We ignore the negative value of n as we can't have a negative number of rows. Therefore, n = 19 is the only valid solution here.

If we wanted to stack 190 logs in this triangular pyramid fashion, then we'll need to have 19 rows. The bottom row will have 19 logs.

----------

Check:

1+2+3+4+5+6+7+8+9+10 = 55

11+12+13+14+15+16+17+18+19 = 135

55+135 = 190

Or you could say,

T(n) = 0.5*n*(n+1)

T(19) = 0.5*19*(19+1)

T(19) = 190

Either way, the answer is confirmed.

8 0
2 years ago
What would be the exact side length of a square with the area of 8 m2
Paraphin [41]

Answer:

2*square root of 2

Step-by-step explanation:

The square root of 8 is equal to 2*square root of 2

5 0
3 years ago
-5(5-3v)=-115<br> Helpp me please
prisoha [69]

we start by opening the brackets so it will be -25 plus 15 v is equals to 115. negative times a negative is a positive so -5 times -3 we we have gotten positive 15v there I hope you understood so our new equation is -25 + 15v is equals to 115 collect the like terms 15v is equals to 115 + 25 15 v is equals to 140 divide both sides by 15 so v is equals to 9 and 1/3

8 0
3 years ago
Multiply (3c+2p)(3c-2p) what is the answer?​
Len [333]

9514 1404 393

Answer:

  9c² -4p²

Step-by-step explanation:

The product of a sum and difference of the same two terms is the difference of their squares:

  (3c +2p)(3c -2p) = 3c(3c -2p) +2p(3c -2p)

  = (3c)² -6cp +6cp -(2p)²

  = (3c)² -(2p)² = 9c² -4p²

4 0
3 years ago
Solve and state any extraneous solutions
Mice21 [21]

\frac{3x}{x - 1}  + 2 =  \frac{3}{x - 1}

\frac{3x}{x - 1} +  \frac{2(x - 1) }{ x - 1}   =  \frac{3}{x - 1}

\frac{3x}{x - 1}  +  \frac{2x - 2}{ x - 1}  =  \frac{3}{x - 1}

\frac{3x + 2x - 2}{ x - 1}  =  \frac{3}{x - 1}

3x + 2x - 2 = 3

5x - 2 = 3

5x = 3 + 2

5x = 5

x =  \frac{5}{5}

x = 1

3 0
3 years ago
Other questions:
  • The total amount of deductions from an employee's gross pay is $83.20. If the gross pay is $378.18, what percent of their gross
    12·2 answers
  • Sec theta = 5/3 and the terminal point determined by quadrant 4
    10·2 answers
  • Vertical angles equal to what
    6·2 answers
  • Mr.anderson is trying to use indirect measurement to determine the height of a flagpole. Mr.anderson is 5.5 feet tall and casts
    10·1 answer
  • The national debt of the united states is 970 billion dollars. the 1980 census showed 226,504,825 people. about how many dollars
    14·1 answer
  • If 42 people work in the plant 5/6 of them are in manufacturing how many workers are in the manufacturing plant
    13·2 answers
  • a mailing tube in the shape of cylinder has a height of 24 inches and a radius of 3 inches. what is the volume, in cubic inches,
    13·1 answer
  • Factor the expression by taking out the greatest common factor.<br><br> 9x^2y - 6xy^2
    11·1 answer
  • NEED HELP WITH THESE
    11·1 answer
  • Q5. Solve for x and y using elimination method.<br>10x +3y = 75, 6x - 5y = 11​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!